Therefore: ∠ ABC+∠ bad = 180.

Because AB = 5, AC = 9, ∠ BCA = 30 and AB/sin∠BCA=AC/sin∠ABC.

Therefore: sin∠ABC=9/ 10.

Therefore: sin∠BAD=sin∠ABC=9/ 10.

And: AB/sin∠ADB =BD/sin∠BAD, ∠ ADB = 45.

Therefore: BD=9√2/2.